Amid growing concern about government leaks, Senate officials have discovered that a hideaway where congressional leaders often discuss national secrets is vulnerable to electronic eavesdropping, it was learned last week.

At the same time, a survey by three committees found that the Senate has what one official termed "the potential for serious security problems" because it has no standardized procedures to protect top-secret documents stored in senators' offices.

The findings resulted from a reassessment of Senate security ordered by Majority Leader Robert J. Dole (R-Kan.) after the arrest last December of a transcriber working under contract to the House Armed Services Committee who allegedly tried to sell a classified transcript to a Soviet agent. And they come at a time when members of Congress are being criticized by administration officials for divulging national secrets to the news media.

Alfred M. Lehn, who heads the Senate office of national security information, said Dole recently ordered improvements in the Senate's secret meeting room, situated directly under the Capitol Rotunda, after experts determined that the decade-old facility was vulnerable to modern surveillance devices.

Lehn said the improvements, which are believed to involve reinforcing the room's lead-lined walls, were necessary even though there was no evidence that the security of the room had been violated.

Lehn said a separate study submitted to Dole found that no one in the Senate has any idea how many classified documents are being stored in senators' offices or how many Senate employes are authorized to read top-secret documents. The report recommends creation of a centralized system to control classified materials.

"The report found there is good cause to believe that we have the potential for serious security problems," Lehn said. "You do have an awful lot of offices that can store classified material -- 120 separate places under the control of 300 to 400 people in four different buildings. We need some central office that will be responsible for all of it."

But Lehn quickly added that the report found "no indication of any breach or attempted breach" of security as a result of the current procedures.

As a result of the study, Lehn said the Senate soon will take steps to determine how many Senate employes have been authorized by the Federal Bureau of Investigation to read classified documents and, if necessary, will reduce the number.

In the House, Michael J. O'Neill, chief counsel of the intelligence committee, said its members have discussed creation of a centralized office to protect secret materials.

O'Neill also said that the special room where the House intelligence panel meets to discuss sensitive matters has been improved regularly over the years to keep pace with the increased capabilities of eavesdropping equipment. He said his committee also has had a system for regularly disposing of outdated classified documents since it was founded in 1977.